Blender Eevee how to render Bloom effect when using transparent background
I found a workaround with composting:
1- Enable Bloom pass in View Layer before rendering

2- In Compositor, Add the Bloom pass to the Alpha of the image, use a ColorRamp node to control the bloom effect, and to convert it at the same time to black and white.

Check the original Alpha in the image above and compare to the next image with Bloom added via the ColorRamp node.

3- now we need to use the outcome as the new Alpha pass instead of the original one, for that, I used a Select Alpha node, linked the original image color pass to the color, the new alpha pass to the alpha.
You can see here how the bloom effect shows on the transparent background, now I can fiddle with the ColorRamp node to get the better result, but I find it easier to temporarily add a background in the compositor using an Alpha Over node, to see the results, then I can remove before final render. I also need to mention that I found it gives better results when I use &quot;Ease&quot; mode in the ColorRamp node, but this depends on the desired effect and the project at hand.